A new branching strategy for time constrained routing problems with application to backhauling

In this paper, we explore a new branching strategy for branch-and-bound approaches based on column generation for the vehicle routing problems with time windows. This strategy involves branching on resource variables (time or capacity) rather than on network flow variables. We also examine criteria for selecting network nodes for branching. To test the effectiveness of the branching strategy, we conduct computational experiments on time window constrained vehicle routing problems where backhauling is permitted only after all the shipments to clients have been made. The branching method proved very effective. In cases where time was the more binding constraint, time-based branching succeeded in decreasing the number of nodes explored by two thirds and the total computation time by more than half when compared to flow-based branching. The computational results also show that the overall algorithm was successful in optimally solving problems with up to 100 customers. It produced an average cost decrease of almost 7% when backhauling was permitted as compared to the cost involved when the client and the distributor routes were distinct.     

Late-Stage Functionalisation of Peptides on the Solid Phase by an Iodination-Substitution Approach

The functionalisation of peptides at a late synthesis stage holds great potential, for example, for the synthesis of peptide pharmaceuticals, fluorescent biosensors or peptidomimetics. Here we describe an on-resin iodination-substitution reaction sequence on homoserine that is also suitable for peptide modification in a combinatorial format. The reaction sequence is accessible to a wide range of sulfur nucleophiles with various functional groups including boronic acids, hydroxy groups or aromatic amines. In this way, methionine-like thioethers or thioesters and thiosulfonates are accessible. Next to sulfur nucleophiles, selenols, pyridines and carboxylic acids were successfully used as nucleophiles, whereas phenols did not react. The late-stage iodination-substitution approach is not only applicable to short peptides but also to the more complex 34-amino-acid WW domains. We applied this strategy to introduce 7-mercapto-4-methylcoumarin into a switchable Zn^II responsive WW domain to design an iFRET-based Zn^II sensor.     

Unicity of the Integrated Density of States for Relativistic Schrödinger Operators with Regular Magnetic Fields and Singular Electric Potentials

We show coincidence of the two definitions of the integrated density of states (IDS) for a class of relativistic Schrödinger operators with magnetic fields and scalar potentials introduced in Iftimie et al. (Publ Res Inst Math Sci 43(3):585–623, 2007; Topics in applied mathematics and mathematical physics, Editura Academiei Române, 2008), the first one relying on the eigenvalue counting function of operators induced on open bounded sets with Dirichlet boundary conditions, the other one involving the spectral projections of the operator defined on the entire space. In this way one generalizes the results of Doi et al. (Math Z 237:335–371, 2001) and Iftimie (Publ Res Inst Math Sci 41(2):307–327, 2005) for non-relativistic operators. The proofs needs the magnetic pseudodifferential calculus developed in Iftimie et al. (Publ Res Inst Math Sci 43(3):585–623, 2007), as well as a Feynman-Kac-Itô formula for Lévy processes (Ichinose and Tamura, Commun Math Phys 105(2):239–257, 1986; Iftimie et al. Topics in applied mathematics and mathematical physics, Editura Academiei Române, 2008). In addition, in case when both the magnetic field and the scalar potential are periodic, one also proves the existence of the IDS.     

Homogénéisation de coques minces piézoélectriques perforées

In this Note we establish the limit constitutive law of a piezoelectric material with periodically perforated microstructures and whose reference configuration is a thin shell with fixed thickness. The justification of the new associated model (we show that the limit global and local problems are more complicated than the intial one) is obtained using the periodic unfolding method introduced by Cioranescu, Damlamian and Griso. To cite this article: M. Ghergu et al., C. R. Mecanique 333 (2005).     

Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data

The present paper is dedicated to the study of the global existence for the inviscid two-dimensional Boussinesq system. We focus on finite energy data with bounded vorticity and we find out that, under quite a natural additional assumption on the initial temperature, there exists a global unique solution. No smallness conditions are imposed on the data. The global existence issues for infinite energy initial velocity, and for the Bénard system are also discussed.